%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC121+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:40:03 PM UTC 2026
% Result : Theorem 0.16s 0.42s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 10 unt; 13 def)
% Number of atoms : 264 ( 21 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 298 ( 118 ~; 113 |; 42 &)
% ( 15 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 87 ( 79 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ( segmentP(V,U)
& neq(U,nil) )
| ~ segmentP(X,W)
| ~ neq(W,nil)
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ( segmentP(V,U)
& neq(U,nil) )
| ~ segmentP(X,W)
| ~ neq(W,nil)
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& segmentP(X,W)
& neq(W,nil)
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& segmentP(X,W)
& neq(W,nil)
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f421,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f422,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( ( segmentP(V,U)
& neq(U,nil) )
| ~ segmentP(X,W)
| ~ neq(W,nil)
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& segmentP(X,W)
& neq(W,nil)
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( ( segmentP(V,U)
& neq(U,nil) )
| ~ segmentP(X,W)
| ~ neq(W,nil)
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& segmentP(X,W)
& neq(W,nil)
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
! [X0,X1,X2,X3] :
( neq(X2,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f430,plain,
! [X0,X1,X2,X3] :
( neq(X1,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f431,plain,
! [X0,X1,X2,X3] :
( segmentP(X0,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ~ segmentP(X2,X3)
| ~ neq(X3,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( neq(X3,nil)
| ~ segmentP(X0,X1)
| ~ neq(X1,nil)
| ~ neq(X2,nil)
| sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f435,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f440,plain,
( sQ1_spl
| ~ neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f435,f438]) ).
fof(f442,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f435,f442]) ).
fof(f461,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f462,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f461]) ).
fof(f482,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f436]) ).
fof(f483,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f482]) ).
fof(f484,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ sP0_prd(X0,X1,nil,X2) ),
inference(resolution,[status(thm)],[f429,f462]) ).
fof(f485,definition,
! [X0,X1,X2] :
( sQ3_spl
<=> ~ sP0_prd(X0,X1,nil,X2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f488,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f491,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f484,f485,f488]) ).
fof(f492,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ sP0_prd(X0,nil,X1,X2) ),
inference(resolution,[status(thm)],[f430,f462]) ).
fof(f493,definition,
! [X0,X1,X2] :
( sQ5_spl
<=> ~ sP0_prd(X0,nil,X1,X2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( ~ sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f492,f493,f488]) ).
fof(f497,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f223]) ).
fof(f498,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f499,plain,
( ~ sQ0_spl
| ~ segmentP(sK50_skl,sK49_skl)
| ~ neq(sK49_skl,nil) ),
inference(resolution,[status(thm)],[f432,f483]) ).
fof(f500,definition,
( sQ6_spl
<=> neq(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ6_spl
| ~ neq(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
( sQ7_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ7_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f499,f500,f503,f435]) ).
fof(f507,plain,
! [X0,X1,X2] :
( sQ6_spl
| ~ sP0_prd(X0,sK49_skl,X1,X2) ),
inference(resolution,[status(thm)],[f502,f430]) ).
fof(f509,plain,
( ~ sQ0_spl
| sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f483,f507]) ).
fof(f510,plain,
( ~ sQ0_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f511,plain,
( ~ sQ1_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f439]) ).
fof(f512,plain,
! [X0,X1] :
( sQ7_spl
| ~ sP0_prd(sK50_skl,sK49_skl,X0,X1) ),
inference(resolution,[status(thm)],[f505,f431]) ).
fof(f513,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f511]) ).
fof(f514,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f515,plain,
( sQ1_spl
| ~ neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f440]) ).
fof(f534,definition,
( sQ12_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ12_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f540,definition,
( sQ14_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( sQ14_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f544,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f421]) ).
fof(f545,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f546,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f422]) ).
fof(f547,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f550,plain,
( sQ1_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f515,f220]) ).
fof(f551,definition,
( sQ15_spl
<=> sK50_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( ~ sQ15_spl
| sK50_skl = nil ),
inference(component_clause,[status(thm)],[f551]) ).
fof(f554,plain,
( sQ1_spl
| sQ15_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f550,f534,f488,f551,f438]) ).
fof(f558,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| neq(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f552,f511]) ).
fof(f559,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f558,f462]) ).
fof(f560,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f559,f488,f551,f438]) ).
fof(f582,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ segmentP(X0,X1)
| ~ neq(X1,nil)
| ~ neq(X2,nil)
| sP0_prd(X0,X1,X2,nil) ),
inference(resolution,[status(thm)],[f433,f462]) ).
fof(f583,definition,
! [X0,X1,X2] :
( sQ18_spl
<=> ( ~ segmentP(X0,X1)
| ~ neq(X1,nil)
| ~ neq(X2,nil)
| sP0_prd(X0,X1,X2,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( ~ sQ4_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f582,f583,f488]) ).
fof(f590,plain,
( ~ sQ0_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f512]) ).
fof(f591,plain,
( ~ sQ0_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f592,plain,
$false,
inference(sat_refutation,[status(thm)],[f441,f445,f491,f496,f498,f506,f510,f514,f545,f547,f554,f560,f586,f591]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC121+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 07:58:46 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.40 % Drodi V4.1.1
% 0.16/0.42 % Refutation found
% 0.16/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.52 % Elapsed time: 0.134422 seconds
% 0.20/0.52 % CPU time: 0.130256 seconds
% 0.20/0.52 % Total memory used: 13.936 MB
% 0.20/0.52 % Net memory used: 13.924 MB
%------------------------------------------------------------------------------